We're pretty sure the mind is what the brain does.
> nor how it works.
We don't need to, for this purpose. This is a low-level dump of all the information stored, to enable (much) later analysis.
As I said, current cryonics is perhaps too crude. But the idea itself is not unsound. IF current procedures are not detailed enough to preserve the details then perhaps throwing a few millions into research to find better cryoprotectants or procedures could solve the problem.
> We've only recently discovered that your unconscious self does stuff before your conscious self decides to do it
I don't see the relevance. Your unconscious self is still made of neurons and other material stuff, not magic.